Circulant matrices and Galois-Togliatti systems

Pietro De Poi, Emilia Mezzetti, Mateusz Michałek*, Rosa Maria Miró-Roig, Eran Nevo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. As an application we solve a conjecture stated in [17] concerning the minimality of GT-systems.

Original languageAmerican English
Article number106404
JournalJournal of Pure and Applied Algebra
Issue number11
StatePublished - Nov 2020

Bibliographical note

Funding Information:
Member of INdAM - GNSAGA and supported by PRIN “Geometry of algebraic varieties” 2015EYPTSB - PE1.Supported by the Polish National Science Centre grant no. 2015/19/D/ST1/01180.This work was started at the workshop “Lefschetz Properties and Jordan Type in Algebra, Geometry and Combinatorics,” held at Levico (Trento) in June 2018. The authors thank the Centro Internazionale per la Ricerca Matematica (CIRM) for its support. We also thank Nati Linial and Amir Shpilka for helpful discussions on the computational complexity aspects and for pointing us to [5].

Publisher Copyright:
© 2020 Elsevier B.V.


  • Circulant matrix
  • Laplace equations
  • Monomial ideals
  • Permanent
  • Togliatti systems
  • Weak Lefschetz property


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